Description Usage Arguments Details Value References See Also Examples

This function estimates the extremal dependence coefficients *χ* and *\bar χ*
by Coles et al. (1999).
It also plots the functions *χ(u)* and *\bar χ(u)* against a grid of values in [0,1]
to analyse the extremal dependence of two variables.

1 2 | ```
depchi.fun(X, Y, thresval = c(0:99)/100, tit = "", indgraph = TRUE,
bothest = TRUE, xlegend = "topleft")
``` |

`X` |
Numeric vector. Values of the first variable. |

`Y` |
Numeric vector. Values of the second variable. |

`thresval` |
Numeric vector. Grid values where the functions |

`tit` |
Character string. A title for the plots. |

`indgraph` |
Logical flag. If it is TRUE, plots are carried out in individual windows.
If it is FALSE, windows with 2 |

`bothest` |
Logical flag. If it is TRUE, two estimated coefficientes (for X given Y and for Y given X) are displayed in the same plot. Otherwise, only the coefficient for Y given X is plotted. |

`xlegend` |
Optional. Label "topleft" or"bottomright". Position where the legend on the graph will be located. |

The extremal dependence between two variables X and Y
is the tendency for one variable to be large, given that the other one is large.
The extremal dependence coefficients *χ* and *\bar χ* are defined as
*χ= \lim_{u \to 1} χ(u)* and *\bar χ(u)= 2log(P(U>u)/log P(U>u, V>u)-1*,
where *χ(u)= P(U>u |V>u)* and (U,V) are the transformed uniform marginals of the variables X and Y.

*χ* is on the scale [0, 1], with the set (0, 1] corresponding to asymptotic
dependence, and the measure *\bar χ* falls within the range [-1, 1], with the set [-1, 1)
corresponding to asymptotic independence. Thus, the complete pair (*χ*, *\bar χ*)
is required as a summary of extremal dependence: (*χ > 0*, *\bar χ =1*) signifies asymptotic
dependence, in which case the value of *χ* determines a measure of strength of dependence within
the class; alternatively, (*χ=0*, *\bar χ <1*) signifies asymptotic independence, in which case the value of
*\bar χ* determines the strength of dependence within this class.
Full details can be found in Coles et al. (1999).

In the *χ* plot, the expected behaviour under independence of X and Y is also plotted.

A list with elements

`chiX ` |
Estimated |

`chiY ` |
Estimated |

`chiBX ` |
Estimated |

`chiBY ` |
Estimated |

`PX ` |
Estimation of the probabilities |

`PY ` |
Estimation of the probabilities |

`PXY ` |
Estimation of the probabilities |

`thresval ` |
Input argument |

Coles, S., Heffernan, J. and Tawn, J. (1999) Dependence measures for extreme value analysis. Extremes, 2, 339-365.

`TestIndNH.fun`

, `DutilleulPlot.fun`

, `CondTest.fun`

1 2 3 4 |

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